What is more, the intrinsic dynamics in von Neumann algebras is further exemplified in the study of statistical mechanics in a background-independent setting [1]}, [2]}. Here, \(\omega \in \mathcal {S}(\mathcal {N})\)  is understood as a state in thermodynamic equilibrium. In the setting of quantum statistical mechanics such states are characterised by the KMS condition [3]}. It is a remarkable fact that \(\sigma ^\omega \)  satisfies the KMS condition for every faithful normal state \(\omega \in \mathcal {S}(\mathcal {N})\)  [4]}. In contrast, no analogue of this condition holds for Jordan algebras [5]}. In effect, time orientations in von Neumann algebras allow to interpret time from a thermodynamical standpoint, encoded in a state of thermodynamic equilibrium [6]}.
